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Published April 7, 2000 | Version public
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Uniformly Bounded Maximal ϕ-Disks, Bers Space and Harmonic Maps

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Abstract

We characterize Bers space by means of maximal ϕ-disks. As an application we show that the Hopf differential of a quasiregular harmonic map with respect to strongly negatively curved metric belongs to Bers space. Also we give further sufficient or necessary conditions for a holomorphic function to belong to Bers space.

Additional Information

© 2000 American Mathematical Society. Received by the editors April 20, 1998 and, in revised form, August 27, 1998 and November 18, 1998. We wish to thank the referee for numerous useful comments and suggestions which greatly improved the exposition of our paper and for pointing out that our results can possibly be of use in a number of popular open problems. We also would like to thank M. Wolf for useful conversations and his interest in this work, A. Baernstein for pointing out to us the Stegenga-Stephenson paper [15] and for helping us to prepare this paper, C.V. Stanojević for his continous encouragement and support during the last few years and B. Hanson for his interest in this work and suggestions concerning the language.

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77226
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CaltechAUTHORS:20170505-114730317

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http://www.jstor.org/stable/2669162 (URL)

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2017-05-05
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2019-10-03
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